Complex SUSY Transformations and the Painlev\'e IV Equation
David Berm\'udez
TL;DR
This paper explores complex supersymmetric transformations of the harmonic oscillator to generate new solvable potentials and derives exact complex solutions to the Painlevé IV equation with specific examples.
Contribution
It introduces explicit complex SUSY transformations for the harmonic oscillator and connects these to novel complex solutions of the Painlevé IV equation.
Findings
Generated new exactly-solvable potentials via complex SUSY transformations.
Derived explicit complex solutions to the Painlevé IV equation.
Provided concrete examples illustrating the solutions.
Abstract
In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlev\'e IV equation with complex parameters. We present some concrete examples of such solutions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.